Patrick Gelß, M.Sc. (*XX.XX.XXXX, Berlin, Germany)
2013- Doctoral research in mathematics, Free University Berlin, Germany. Focus: “Tensor Decomposition of the Chemical Master Equation”
2006-2013 Undergraduate studies of mathematics and physics, Free University Berlin, Germany Diploma thesis: “Transition Path Theory for Markov Jump Processes”
In my diploma thesis I was engaged in the Transition Path Theory (TPT). In this context, I examined the behavior of continuous-time Markov chains on discrete state-spaces depending on pertubations of the infinitesimal generator and on different reactant and product sets, i.e. on certain starting and terminal points of a random walker within the state-space. I directed my attention to possible trajectories between these points, their distribution and the corresponding current as well as to the transition rates. Also, I involved the fields of graph theory and stochastic theory in my work and made references to various branches of science, e.g. queuing theory, electrical resistor networks and the concepts of navigation.
Since the approval for a scholarship of the BMS, I have been focusing on the tensor decomposition of the Chemical Master Equation (CME). In this context, I am interested in various tensor formats as the Tensor Train (TT) and Quantized Tensor Train format (QTT), that provide promising new approaches to avoid the curse of dimensionality and solve the CME directly on a truncated state-space.
My expertise includes modeling of biochemical systems, multi-linear algebra, numerical algorithms for solving ordinary differential equations and linear systems given in tensor formats.